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Full text of "Analytical Mechanics"

MOTION OF A PARTICLE                       115
g must be replaced by (-g) before they are applied to the motion of bodies which are projected vertically upwards.
PROBLEMS.
1.   A steel plate weighing 10 pounds is placed on a perfectly smooth and perfectly horizontal sheet of ice.   The plate is then moved by means of a string, cne end of which is fastened to the plate, and the string is pulled in a direction parallel to the surface of the ice.    Is it necessary to apply a force to the string in order to give the plate a desired velocity? Why?   What will the magnitude of the force depend upon?
2.   In the preceding problem the block is given a velocity of 100 -
sec.
in 5 seconds.    Find the tension of the string supposing it to be constant. How far will the plate have traveled in the meantime ?
3.   In the preceding problem the string is just strong enough to support half the weight of the plate.   What is the shortest time in which the plate can be pulled through a distance of 162 feet?
4.   In the preceding problem suppose the contact to be rough and to have a coefficient of friction equal to 0.1.
6.  A bullet is fired with a muzzle velocity of 500 meters.   Find the
sec.
average acceleration, supposing the length of the barrel to be 80 cm.
6.   A stone is sent gliding over a horizontal sheet of ice with a speed
of 10 -i.    How far and how-long will it move if the coefficient of sec.
friction is 0.1?
7.   An elevator starts from rest and rises to a height of 100 feet in 10 seconds, with a constantly increasing velocity.   Find the increase.in pressure exerted on the feet of a man in the elevator who weighs 150 pounds.
8.   A man can just lift 350 pounds when on the ground.   How much
can he lift when in an elevator descending with an acceleration of 4 -2?
sec.
9.   An elevator starts from rest and rises 100 feet in five seconds, with a constant acceleration.   Find the tension of the rope which pulls it up
if the elevator weighs 2000 pounds; neglect the frictional forces.
rji
10.   A body is projected vertically upward with a velocity of 50 - at
sec.
the edge of a pit 200 feet deep.   When will it strike the bottom?
11.   What is the lowest level, over the enemy's camp, to which a balloon can safely descend, if the enemy is provided with guns which have muzzle velocities of 2000 feet per second?